Question

A body of mass m performs uniform circular motion along a circular path of radius $r$ with velocity $v$ . If its angular momentum is $L$ ,then the centripetal force acting on it is:

• A. $L^2/m{r}^2$
• B. $L^2/m{r}^3$
• C. $L^2/mr$
• D. $L^2/m^3$

Answer 1

Answer: (B)

$L^2/m{r}^3$

Lets consider,

$m=$ mass of body performing circular motion

$L=$ angular momentum

$r=$ radius of circular path

$v=$ velocity of the particle

The angular momentum ,

$L=mvr$

$v=\frac{L}{mr}$. . . . . . .(1)

The centripetal force,

$f_c=\frac{m{v}^2}{r}$. . . .(2)

Substitute equation (1) in equation (2), we get

$f_c=\frac{m}{r}(\frac{L}{mr}{)}^2$

$f_c=\frac{L^2}{m{r}^3}$

The correct option is B.